"I disagree that the RSC should be forced to employ equal numbers of female and male actors," he said. "There has to be some artistic exceptions to terms of employment law. We've got to allow directors to do what they think is right.

"Not all productions are going to be in an aesthetic range that will welcome cross-gender casting. Casting more women to play men could make it incoherent to a mainstream audience."

He added: "People going to see a Shakespeare play expect realism and expect men [playing male roles.] This should be about realism."

She added the RSC "should be just told that they have to have a 50/50 employment spread, then work out how to do the plays", which could involve gender-blind casting.

However, Prof. Dobson, who co-founded the European Shakespeare Research Association and who reviewed every major production of a Shakespeare play in England during 1999 and 2007 for respected Shakespeare journals, said play roles should be cast on merit alone and gender should not come into it.

He did, however, call for "an equal number of all-female casts as there are all-male casts" in the UK.

"But the RSC is rather different to the Donmar Warehouse, which is all about taking important artistic risks," he said.

He added that the first Shakespeare all-female play, a version of The Winter's Tale, was produced in 1774 – meaning the concept is not "particularly new" – but he "applauds" theatre companies for running all-female productions.

Elsewhere, Profsesor Liz Schafer, a Shakespeare scholar at the Royal Holloway University of London, said: "There’s little point in trying to force an institution like the RSC to employ more women, but they could certainly be encouraged to, and this would benefit the whole company. There are many roles in Shakespeare that could be played by women: Franciscos can easily become Franciscas, Gonzalos can become Gonzalas, and early career performers playing third servant on the left can be women just as well as men."

As far as star roles are concerned, there’s nothing new in the idea of having women play Shakespeare’s great roles, she adds. Women from Sarah Siddons and Sarah Bernhardt to Frances de la Tour have played Hamlet. Women have also played Richard III, Romeo, Lear and Falstaff, she says.

"I remember with great fondness a production of A Midsummer Night’s Dream which featured Dawn French’s rather remarkable Bottom. A few years ago the RSC produced a Twelfth Night, directed by Neil Bartlett, which had Sir Toby Belch, Sir Andrew Aguecheek and Fabian all played by women. But a particularly interesting test case is the role of the Chorus in Henry V; there’s no reason why this non-gender specific role should be played by a man and nineteenth century choruses were often played by a leading actress."

Prof. Schafer adds that Greg Doran, the chief associate director of the RSC, has a "great opportunity to move the RSC forward in terms of employing women, giving women more roles, developing more women’s careers and, thereby, increasing the RSC’s skills base".

But it is crucial that theatre directors of Shakespeare plays retain artistic integrity, Prof. Dobson explains. The Oxford-educated academic said directors should have the choice to cast female actors into male roles, but that forcing them could be at the expense of the performance. When asked if a play's performance would suffer as a result of being forced to employ more women into roles, Prof. Dobson said: "It might do."

Prof. Dobson did, however, say that there should be more women behind the stage. "I completely understand that women are under-represented in management professions in the theatre," he said.

"But there should be a range of choices available to directors casting plays; there is always a problem when artistic considerations come up against social legislation. Shakespeare wrote plays largely with specific male parts to be played by men."

So what would Shakespeare make of the current debate on employing more women? "He'd be thrilled at the opportunity to have women in his plays; he didn't have that option in his day. He may have wrote plays differently if he could cast women," he said.